I know I'm in the minority on this one, but I prefer minutes because its a concrete concept...tiring, mostly fresh, etc. seemed too abstract to me to feel comfortable basing a substitution pattern off of. It also allows me to better limit the amount of time my one-dimensional players (usually defensive stoppers whose sole job it is to come in and make it difficult to score, maybe come up with a steal now and then and for god sakes try not to turn the ball over) get on the floor.
The drawback with minutes is the computer will play for whatever 4-min. target range you're looking at. If you've got it set for 29-33, for instance, and your player gets in early foul trouble and sits for most of the first half, then he's going to try and reach his minutes by playing the entire second half without rest if need be.
I usually compensate for this by under-setting my minutes so that the collective range adds up to 150-180ish. This minimizes the foul issue impact should it arise. If I'm in a close game, those "extra" unassigned minutes are given to my starters by the computer AI. In blowouts, they're distributed among the backups, just like I'd like them to be. As best I can tell, this still seems the case under the new engine.
Like I said, I know I'm in the minority from asking around, but that's my rationale for going minutes vs. fatigue.